In a conventional device of this type to which the invention is directed, the control slide valve driven by the pressure of the reservoir, enters its starting position in which it interrupts the direct communication between the pressure chamber of the fuel injection nozzle and the feed line leading to the injection pump relatively quickly, so that too little time is available for the required pressure relief of the pressure chamber of the nozzle toward the injection pump. This leads to dribbling with a consequent impairment of the exhaust gas and a gumming up of the nozzle injection orifices with carbon.